Focusing Surface-Acoustic-Wave Resonators on Thin-Film Lithium Niobate with Transverse-Mode Suppression

Abstract

Surface-acoustic-wave (SAW) resonators are a promising platform for constructing hybrid quantum systems, where confined acoustic waves enable strong interaction with various physical systems. Focusing SAW resonators, reducing mode volume while suppressing diffraction losses, have recently been investigated for application in such hybrid systems. However, the resonator leads to additional transverse-mode resonances, which cause undesired responses. In this work, we develop single-mode focusing SAW resonators on a thin-film lithium niobate on sapphire. A film thinner than the SAW wavelength allows a highly confined acoustic-wave mode to be localized on the substrate surface. By using contoured electrodes following a two-dimensional Gaussian beam shape, we make the SAW mode focused to nearly a diffraction-limited and confirm it via optical imaging. The apodization technique applied to the interdigitated transducer electrodes suppresses the excitation of higher-order transverse modes.

Figures (9)

• Figure 1: (a) Schematic image of a 2-port focusing SAW resonator. The yellow arrow indicates the effective mirror distance $d$ of two Bragg mirrors. The coordinate axes, $\{x,y,z\}$, and corresponding crystal axes of LN, $\{\mathrm{X, Y, Z}\}$, used in this work are shown in the inset. (b)(c) Normalized displacement profile of the fundamental ($l=0$) and higher-order transverse ($l=2$) modes, respectively. Blue and orange solid curves respectively depict the mode width $\pm w(x)$ and $\pm 2w(x)$, respectively, where $w_0 \equiv w(x=0)$ is set to $\lambda$. (d)(e) Cross-sections of the normalized displacement at the mode waist $x = 0$ for the two modes.
• Figure 2: (a) Simulated dispersion relation of the SAW modes in a LN thin film with a thickness of $0.8µm$ on a sapphire substrate. The gray area shows the continuum of bulk-acoustic-wave modes in sapphire. $p$ = 1µm is the unit length of the model along the X-axis. The $k^2$-dependent dispersion at $k\sim0$ is an artifact due to the finite length of the model along the Y axis, which is comparable to the mode wavelength in this region. (b)(c) Displacements $u$ of Love and Rayleigh modes at $k = \pi/p$, respectively. LN and Sa represent the region of lithium niobate and sapphire, respectively (d)(e) Simulated crystal anisotropy of the acoustic phase velocity $v_\mathrm{p}$ and electromechanical coupling $K^2$ of the SAW modes.
• Figure 3: (a) Optical microscope image of a fabricated device. The orange dashed lines show the designed electrode length of $\pm 2w(x)$. (b) Microwave transmission spectra $|S_{21}|^2$ between two IDTs. The black arrows indicate the resonance peaks attributed to transverse modes. Circles and a triangle indicate fundamental and spurious modes, respectively. (c) Shift of the resonant frequencies of the higher-order modes. The transmission spectra $|S_{21}|$ as a function of the frequency separation $\Delta f$ from the fundamental-mode frequency at around 2.21GHz are measured in 17 devices with different $w_0$. The white dashed lines are the frequency separations between the fundamental ($l=0$) and higher-order ($l>0$) modes $\Delta f_{l0}$, for $l$ =0, 2, 4, 8, and 12, calculated from Eq. (\ref{['delta frequency']}).
• Figure 4: Optical imaging of focusing SAW resonators. (a) Optical power measured with a power meter for the SAW resonator with $w_0 = 2µm$ at the resonance frequency of 2.159GHz. (b) Amplitude, and (c) phase of the optical signal measured with a lock-in amplifier. (d) Optical power, (e) amplitude, and (f) phase for the SAW resonator with $w_0 = 8µm$ at the resonance frequency of 2.148GHz. (g) Amplitude and (h) phase at 2.159GHz, corresponding to the $l=2$ transverse mode. The scanning areas are the same as in (d)--(f). Dashed lines in (a)--(c) and (d)--(h) depict the mode width $\pm w(x)$ for $w_0 = 2µm$ and $8µm$, respectively
• Figure 5: (a) Amplitude profile along the $y$-axis at the mode waist of the device with $w_0 =$ 2µ m. The solid curve shows the fit to a Gaussian function. (b) Estimated half mode waist $w_0^\mathrm{est}$ vs. the designed value $w_0^\mathrm{design}$ of the focused SAW mode at the waist. Error bars show the fitting errors. The dashed line shows the design value.